$f(n) = -3n^{3}+2n^{2}+4(g(n))$ $h(n) = n^{2}$ $g(n) = -n^{2}+4(h(n))$ $ f(h(-2)) = {?} $
Solution: First, let's solve for the value of the inner function, $h(-2)$ . Then we'll know what to plug into the outer function. $h(-2) = (-2)^{2}$ $h(-2) = 4$ Now we know that $h(-2) = 4$ . Let's solve for $f(h(-2))$ , which is $f(4)$ $f(4) = -3(4^{3})+2(4^{2})+4(g(4))$ To solve for the value of $f$ , we need to solve for the value of $g(4)$ $g(4) = -4^{2}+4(h(4))$ To solve for the value of $g$ , we need to solve for the value of $h(4)$ $h(4) = 4^{2}$ $h(4) = 16$ That means $g(4) = -4^{2}+(4)(16)$ $g(4) = 48$ That means $f(4) = -3(4^{3})+2(4^{2})+(4)(48)$ $f(4) = 32$